mine would shake on the freeway around 110...turns out it was toeing out, on one side more than the other...not sure why, just wear and tear on bushes I suspect.. Probably caused by 200,000kms of my aggressive turning to the left or something I dunno..lol
...once aligned it was fine, even with the crappy tyres..
If you have issues best thing is usually take it to a alignment shop..I mean we can all sit here and play guessing games or you can just go spend 50$ and find out the problem and hopefully have it rectified,,,